Finite Group Databasebeta

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C22×C5×#10625202 #28414932

order14820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×#10625202

Splittings

Fitting, socle, HallC22×C5×C13×C19 ⋊ C3
derived, HallC13×C19 ⋊ C22×C3×C5
HallC5×C13×C19 ⋊ C22×C3
HallC22×C13×C19 ⋊ C3×C5
HallC22×C5×C19 ⋊ C13⋊C3
HallC22×C5×C13 ⋊ C19⋊C3
HallC5×C19 ⋊ C22×C13⋊C3
HallC22×C19 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C22×C19⋊C3
HallC22×C13 ⋊ C5×C19⋊C3
SylowC19 ⋊ C22×C5×C13⋊C3
SylowC13 ⋊ C22×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C5#10625202
commutator, cosocle, hypocenterC13×C19C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C13×C19C3
LCSG ▷ C13×C19
UCSC1 ◁ C22×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4940

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 218);